Dimensionality-induced phonon softening: effect on electron-phonon coupling and transport

Classical elasticity theory predicts that finite-thickness unstrained materials should exhibit a quadratic flexural phonon mode. However, state-of-the-art computational methods have been largely inconsistent in yielding such a behavior for the phonon dispersion curves of two-dimensional (2D) materials and their heterostructures. Given the enormous attention 2D materials have received in recent decades, it is imperative to understand the impact of this phonon softening on ab initio predicted electron-phonon coupling strength and resultant transport properties. Recently, a new formulation of phonon calculations based on internal rather than Cartesian coordinates has observed that capturing rotational invariance in addition to translation invariance captures the quadratic mode correctly. Here, we investigate the role of rotational invariance on predicted phonon dispersion curves rigorously, and systematically quantify its impact on electron-phonon scattering rates. We show that the cross-over from a linear to quadratic dispersion of the transverse acoustic branch strongly affects transport properties such as electrical and thermal conductivity when we move from bulk to few- and single-layer materials.